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<H3>improper_style class2 command 
</H3>
<H3>improper_style class2/omp command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>improper_style class2 
</PRE>
<P><B>Examples:</B>
</P>
<PRE>improper_style class2
improper_coeff 1 100.0 0
improper_coeff * aa 0.0 0.0 0.0 115.06 130.01 115.06 
</PRE>
<P><B>Description:</B>
</P>
<P>The <I>class2</I> improper style uses the potential
</P>
<CENTER><IMG SRC = "Eqs/improper_class2.jpg">
</CENTER>
<P>where Ei is the improper term and Eaa is an angle-angle term.  The 3 X
terms in Ei are an average over 3 out-of-plane angles.
</P>
<P>The 4 atoms in an improper quadruplet (listed in the data file read by
the <A HREF = "read_data.html">read_data</A> command) are ordered I,J,K,L.  X_IJKL
refers to the angle between the plane of I,J,K and the plane of J,K,L,
and the bond JK lies in both planes.  Similarly for X_KJLI and X_LJIK.
Note that atom J appears in the common bonds (JI, JK, JL) of all 3 X
terms.  Thus J (the 2nd atom in the quadruplet) is the atom of
symmetry in the 3 X angles.
</P>
<P>The subscripts on the various theta's refer to different combinations
of 3 atoms (I,J,K,L) used to form a particular angle.  E.g. Theta_IJL
is the angle formed by atoms I,J,L with J in the middle.  Theta1,
theta2, theta3 are the equilibrium positions of those angles.  Again,
atom J (the 2nd atom in the quadruplet) is the atom of symmetry in the
theta angles, since it is always the center atom.
</P>
<P>Since atom J is the atom of symmetry, normally the bonds J-I, J-K, J-L
would exist for an improper to be defined between the 4 atoms, but
this is not required.
</P>
<P>See <A HREF = "#Sun">(Sun)</A> for a description of the COMPASS class2 force field.
</P>
<P>Coefficients for the Ei and Eaa formulas must be defined for each
improper type via the <A HREF = "improper_coeff.html">improper_coeff</A> command as
in the example above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands.
</P>
<P>These are the 2 coefficients for the Ei formula:
</P>
<UL><LI>K (energy/radian^2)
<LI>X0 (degrees) 
</UL>
<P>X0 is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian^2.
</P>
<P>For the Eaa formula, each line in a
<A HREF = "improper_coeff.html">improper_coeff</A> command in the input script lists
7 coefficients, the first of which is "aa" to indicate they are
AngleAngle coefficients.  In a data file, these coefficients should be
listed under a "AngleAngle Coeffs" heading and you must leave out the
"aa", i.e. only list 6 coefficients after the improper type.
</P>
<UL><LI>aa
<LI>M1 (energy/distance)
<LI>M2 (energy/distance)
<LI>M3 (energy/distance)
<LI>theta1 (degrees)
<LI>theta2 (degrees)
<LI>theta3 (degrees) 
</UL>
<P>The theta values are specified in degrees, but LAMMPS converts them to
radians internally; hence the units of M are in energy/radian^2.
</P>
<HR>

<P>Styles with a <I>cuda</I>, <I>gpu</I>, <I>omp</I>, or <I>opt</I> suffix are functionally
the same as the corresponding style without the suffix.  They have
been optimized to run faster, depending on your available hardware, as
discussed in <A HREF = "Section_accelerate.html">Section_accelerate</A> of the
manual.  The accelerated styles take the same arguments and should
produce the same results, except for round-off and precision issues.
</P>
<P>These accelerated styles are part of the USER-CUDA, GPU, USER-OMP and OPT
packages, respectively.  They are only enabled if LAMMPS was built with
those packages.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info.
</P>
<P>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <A HREF = "Section_start.html#start_7">-suffix command-line
switch</A> when you invoke LAMMPS, or you can
use the <A HREF = "suffix.html">suffix</A> command in your input script.
</P>
<P>See <A HREF = "Section_accelerate.html">Section_accelerate</A> of the manual for
more instructions on how to use the accelerated styles effectively.
</P>
<HR>

<P><B>Restrictions:</B>
</P>
<P>This improper style can only be used if LAMMPS was built with the
CLASS2 package.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info on packages.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "improper_coeff.html">improper_coeff</A>
</P>
<P><B>Default:</B> none
</P>
<HR>

<A NAME = "Sun"></A>

<P><B>(Sun)</B> Sun, J Phys Chem B 102, 7338-7364 (1998).
</P>
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